I am in the process of testing the measurement model that will be used when I test structural relationships between latent variables of interest. If I mix binary and continuous dependent variables together as measures of a latent factor and specify that the binary dependent variables are categorical, what problems or misunderstandings does this method lead to? For example, I tried running Mplus using the default analysis procedure (general-ML) treating both the binary and continuous variables as continuous. I then ran the analysis again, where the only change was to specify that the binary variables are categorical. I think that Mplus automatically switches to WLSMV according to the table on page 38. In comparing the results drawn from these two analyses, model fit was about the same but, the regression coefficients between the latent factor and dependent variables were much higher when the dichotomous variables were specified as categorical. What do you recommend?

When you treat all of the variables as continuos, the factor loadings are ordinary linear regression coefficients. When you treat them as categorical, the factor loadings are probit regression coefficients and therefore not on the same scale. I would generally recommend treatng dichotomous items as categorical particulary if they are far from a 50/50 split. The loadings are higher when you treat the variables as dichotomous because correlations are attenuated when categorical variables are treated as continuous.

If I fix the scale of the latent factor to the continuous variable and include categorical indicators (binary), I will be using indicators measured on different scales. Is it correct that Mplus will compute regression coefficients for the continuous variable using ordinary linear regression and compute regression coefficients for the binary variables using probit regression. Thanks for your help.

Mplus can accommodate a combination of continuous and categorical factor indicators. The factor loadings for the categorical indicators and probit regression coefficients. The factor loadings for the continouous indicators are ordinary linear regression coefficients. The estimator is not OLS but WLSMV. These will result in the same estimates in large samples.

Are there any situations where you recommend treating binary variables as continuous? In another post, you referenced small sample size as a reason to do this. I have 199 observations and am using WSLMV. My model looks like this: L1 by f1 f2 f3 f4 f5 X1 on L1 Y1 on X1 X2 X3 X4 X5

I am trying to determine the best way to treat binary variable X1, which does have about a 50-50 split.